The frequency selecting element is an important component in the electronic industry. The general wireless communication system uses different frequencies, and frequency selecting elements of different specifications. For example, the filter in the wireless communication receiver is for filtering out the interfering frequencies so as to relax the restriction on the signal dynamic range of the circuit, and the circuit can be implemented to a low power consumption and low cost specification. Furthermore, the communication quality can be improved by filtering out the interference signals, thereby increasing the signal-to-noise ratio (SNR). In addition to communication systems, the filters of various specifications and types are also used in consumer electronic products. In all these applications, it is important for the filter to be able to precisely select the frequency.
The main function of a filter is to select the frequency on the frequency spectrum. Therefore, the filter usually includes frequency selecting elements, such as inductor and capacitor. FIG. 1A shows a typical RC circuit, which is a main component of a low pass filter. The relation between the output voltage Vout and input voltage Vin is
  Vout  =            1              sCR        +        1              ⁢          Vin      .      FIG. 1B shows a typical LC circuit, which is also a main component of a low pass filter. The relation between the output voltage Vout and input voltage Vin is
  Vout  =            1                                    s            2                    ⁢          LC                +        1              ⁢          Vin      .      
The output voltage Vout of the RC circuit and the LC circuit forms the low pass response with respect to the input voltage Vin, as shown in FIG. 1C, where the x-axis is the frequency, and the y-axis is the ratio of the Vout versus Vin. The frequency selectable characteristic is the core of the filter component.
When the filter is realized in an IC, the inductor and the resistor of FIGS. 1A & 1B will be substituted by other means because of the operating frequency and the operating characteristics.
FIG. 2A shows the use of an operation amplifier 203 to implement a higher order filter in an RC filter. The operation amplifier can serve the purpose of isolation and buffering in a high order system, simplifies the design and improves the performance. However, it is hard for the operation amplifier to have a sufficient bandwidth.
FIG. 2B shows a transadmittance filter. As shown in FIG. 2B, the transadmittance filter uses a transconductor 205 to convert the voltage signals, Vin and Vin_, into current signals, to charge and discharge the capacitor C, then to convert into output voltage signal Vout. This forms the frequency selection mechanism. The transadmittance filter can compensate for the problems of higher operating frequency and 20 insufficient bandwidth encountered by the operation amplifier 203 of FIG. 2A.
FIG. 2C shows a switch capacitor filter. The filter uses two switches 207, 208 for switching between capacitors C1, C2, and controlling the charging and discharging to form the frequency selection mechanism. The frequency selection precision is good, but this design is a discrete time type and subjected to additional noise and interference. In addition, this type of filter must be used together with other circuit component, and cannot be used in all systems.
In contrast to the switch capacitor filter being a discrete time filter, the RC filter and the transadmittance filter are both continuous time filters.
FIG. 3A shows a response figure of a typical low pass filter, where the x-axis is the frequency and the y-axis is the output voltage. As shown in FIG. 3A, the cut-off frequency is about 250 MHz. The cut-off frequency is an important design parameter for the filter. When the cut-off frequency is too high, the filter is unable to filter out the unwanted noise or interference signals outside of the operation bandwidth; thus, the SNR is reduced and the communication quality is poor. On the other hand, when the cut-off frequency is too low, a part of the operation bandwidth will be cut off; thus, the system may not function normally. In other words, the frequency response precision of a filter will greatly affect the operation of the system.
The variation of the manufacture parameter is inevitable in the IC design. With the variation of temperature and the power supply voltage, the characteristic variation will be even greater. FIG. 3B shows the frequency response variation of the filter caused by the manufacturing variation. As shown in FIG. 3B, the filter is designed to have a cut-off frequency at 250 MHz in an ideal manufacturing process 301. However, the process, temperature, and DC power supply variations make the frequency response to generate too high or too low variation, shown as the frequency response curves 303, 305, respectively.
If no compensation mechanism is added to the filter, the distortion in the frequency response will lead to the malfunction of the system, or poor performance. Therefore, the continuous time filter requires a compensation mechanism. The discrete time filter is usually immune to the variations; therefore, no additional compensation mechanism is required. But, the discrete time filter is not applicable to all types of systems.
Among the current wireless communication systems, the multi-standard communication systems are widely used, for example, 3G and 2G, or 2G and WiFi dual-standard systems. FIG. 4 shows a system block diagram of a dual-standard RF sub-system. As shown in FIG. 4, the RF front-end circuit includes three RF elements of different operation frequencies, i.e., GSM900 channel, DSC/PCS channel, and CDMA2000 channel. The RF sub-system includes large-area channel filters 401, 402. Channel filter 401 is the filter for GSM900 channel and DSC/PCS channel, with the cut-off frequency at 150 KHz. Channel filter 402 is for CDMA2000 channel, with the cut-off frequency at 600 KHz. To integrate the GSM/DSC and CDMA2000 wireless communication modules, the system must use different filters 401, 402. This type of design does not only require a larger chip area, but also raises the manufacturing cost.